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RENORMALIZATION TRANSFORMATIONS IN THE VICINITY OF 1ST-ORDER PHASE-TRANSITIONS - WHAT CAN AND CANNOT GO WRONG

VANENTER, ACD; FERNANDEZ, R; SOKAL, AD; (1991) RENORMALIZATION TRANSFORMATIONS IN THE VICINITY OF 1ST-ORDER PHASE-TRANSITIONS - WHAT CAN AND CANNOT GO WRONG. PHYS REV LETT , 66 (25) 3253 - 3256.

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Abstract

We reconsider the conceptual foundations of the renormalization-group (RG) formalism. We show that the RG map, defined on a suitable space of interactions, is always single valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the other hand, we prove in several cases that near a first-order phase transition the renormalized measure is not a Gibbs measure for any reasonable interaction. It follows that the conventional RG description of first-order transitions is not universally valid.

Type:Article
Title:RENORMALIZATION TRANSFORMATIONS IN THE VICINITY OF 1ST-ORDER PHASE-TRANSITIONS - WHAT CAN AND CANNOT GO WRONG
Keywords:LATTICE SYSTEMS, MATHEMATICAL PROPERTIES, GAUGE-THEORY, PRESSURE, DIAGRAMS
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics

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